Put-Call Parity





Kerry Back

Put-Call Parity

  • Protective put portfolio is same as call with cash
  • Cash = PV of strike
  • Stock ends up \(\Rightarrow\)
    • With put, keep underlying
    • With call, exercise to get underlying
  • Stock ends down \(\Rightarrow\)
    • With put, exercise to get cash
    • With call, keep cash

Prices of puts and calls

  • Put-call parity implies that underlying price + put premium should equal PV of strike plus call premium
  • Equivalently, put premium = call premium + PV of strike - underlying price
  • Equivalently, call premium = put premium - PV of strike + underlying price
  • Actually, this is true only for European options on stocks that don’t pay dividends before the option maturity.